Abstract The possibility of constructing statistical models for prediction of alveolar oxygen and carbon dioxide tensions has been investigated in 20 mechanically ventilated patients in acute respiratory failure (ARF). Linear multiple regression analysis using PaCO 2 and PaO 2 as dependent variables was used to construct (a) models for individual patients, (b) models for specific diagnostic groups and (c) general models (all patients). The coefficient of determination ( R 2) was highest for the individual patient models (0.32–0.99) and lowest for the general models (0.28–0.49). In order to achieve a high predictive accuracy, models matching individual patients should be constructed on the basis of initial invasive blood gas measurement. Statistically derived models may bring better understanding of the behaviour of factors influencing arterial gas tensions in ARF and may be of value in the management of patients on mechanical ventilation.